There is known a fastening device in which a socket is fixed to a wall, for example, and a plug is inserted into the socket and locked therein, thereby attaching to the wall a desired article such as a cover of lighting equipment previously attached to the plug. In order that the plug and the socket shall be surely connected together without play, the rear surface of the forward end head portion of the plug is formed into a slant surface that is sloped or extends radially inward toward the rear end thereof. A locking element fitted to the socket is resiliently pressed against the slant surface radially inward, thereby displacing the plug forward (i.e. drawing the plug into the socket; for example, see Japanese Patent Application Publication No. 2001-182726). In this type of fastening device, however, if an excessive pulling force is applied to the plug, the slant surface of the plug acts to displace the locking element radially outward, which may lead to a situation that the plug undesirably comes out of the socket.